Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,4,Mod(361,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.k (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(104.079369250\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 27x^{6} + 10x^{5} + 446x^{4} + 62x^{3} + 3061x^{2} + 2142x + 14161 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{8}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 588) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(2.46576 - 4.27083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.361 |
Dual form | 1764.4.k.bd.1549.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.32752 | − | 9.22754i | −0.476508 | − | 0.825336i | 0.523129 | − | 0.852253i | \(-0.324764\pi\) |
−0.999638 | + | 0.0269168i | \(0.991431\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.32699 | + | 5.76252i | −0.0911933 | + | 0.157951i | −0.908014 | − | 0.418941i | \(-0.862401\pi\) |
0.816820 | + | 0.576892i | \(0.195735\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 75.9335 | 1.62001 | 0.810006 | − | 0.586422i | \(-0.199464\pi\) | ||||
0.810006 | + | 0.586422i | \(0.199464\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −52.1435 | + | 90.3152i | −0.743921 | + | 1.28851i | 0.206776 | + | 0.978388i | \(0.433703\pi\) |
−0.950697 | + | 0.310121i | \(0.899631\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −42.7472 | − | 74.0402i | −0.516151 | − | 0.894000i | −0.999824 | − | 0.0187511i | \(-0.994031\pi\) |
0.483673 | − | 0.875249i | \(-0.339302\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −34.3366 | − | 59.4728i | −0.311291 | − | 0.539171i | 0.667351 | − | 0.744743i | \(-0.267428\pi\) |
−0.978642 | + | 0.205572i | \(0.934095\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.73498 | − | 9.93327i | 0.0458798 | − | 0.0794662i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −87.7843 | −0.562108 | −0.281054 | − | 0.959692i | \(-0.590684\pi\) | ||||
−0.281054 | + | 0.959692i | \(0.590684\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −31.3841 | + | 54.3589i | −0.181831 | + | 0.314940i | −0.942504 | − | 0.334195i | \(-0.891536\pi\) |
0.760673 | + | 0.649135i | \(0.224869\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −21.1047 | − | 36.5544i | −0.0937726 | − | 0.162419i | 0.815323 | − | 0.579006i | \(-0.196559\pi\) |
−0.909096 | + | 0.416587i | \(0.863226\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −313.904 | −1.19570 | −0.597848 | − | 0.801609i | \(-0.703977\pi\) | ||||
−0.597848 | + | 0.801609i | \(0.703977\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 306.591 | 1.08732 | 0.543659 | − | 0.839306i | \(-0.317038\pi\) | ||||
0.543659 | + | 0.839306i | \(0.317038\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 107.541 | + | 186.266i | 0.333754 | + | 0.578079i | 0.983245 | − | 0.182291i | \(-0.0583513\pi\) |
−0.649491 | + | 0.760369i | \(0.725018\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 262.512 | − | 454.684i | 0.680354 | − | 1.17841i | −0.294519 | − | 0.955646i | \(-0.595159\pi\) |
0.974873 | − | 0.222762i | \(-0.0715073\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 70.8986 | 0.173818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 180.246 | − | 312.195i | 0.397729 | − | 0.688886i | −0.595717 | − | 0.803195i | \(-0.703132\pi\) |
0.993445 | + | 0.114308i | \(0.0364652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −400.363 | − | 693.449i | −0.840348 | − | 1.45553i | −0.889601 | − | 0.456739i | \(-0.849017\pi\) |
0.0492530 | − | 0.998786i | \(-0.484316\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −404.537 | − | 700.679i | −0.771949 | − | 1.33705i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20.1143 | − | 34.8390i | 0.0366769 | − | 0.0635262i | −0.847104 | − | 0.531427i | \(-0.821656\pi\) |
0.883781 | + | 0.467900i | \(0.154989\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 298.781 | 0.499419 | 0.249709 | − | 0.968321i | \(-0.419665\pi\) | ||||
0.249709 | + | 0.968321i | \(0.419665\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −258.563 | + | 447.844i | −0.414555 | + | 0.718030i | −0.995382 | − | 0.0959971i | \(-0.969396\pi\) |
0.580827 | + | 0.814027i | \(0.302729\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 611.233 | + | 1058.69i | 0.870494 | + | 1.50774i | 0.861486 | + | 0.507781i | \(0.169534\pi\) |
0.00900832 | + | 0.999959i | \(0.497133\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1328.55 | −1.75696 | −0.878479 | − | 0.477782i | \(-0.841441\pi\) | ||||
−0.878479 | + | 0.477782i | \(0.841441\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1111.18 | 1.41794 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −319.969 | − | 554.203i | −0.381086 | − | 0.660060i | 0.610132 | − | 0.792300i | \(-0.291116\pi\) |
−0.991218 | + | 0.132240i | \(0.957783\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −455.473 | + | 788.902i | −0.491900 | + | 0.851996i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1425.65 | 1.49230 | 0.746149 | − | 0.665779i | \(-0.231901\pi\) | ||||
0.746149 | + | 0.665779i | \(0.231901\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −496.085 | + | 859.244i | −0.488736 | + | 0.846515i | −0.999916 | − | 0.0129585i | \(-0.995875\pi\) |
0.511180 | + | 0.859473i | \(0.329208\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −133.786 | − | 231.724i | −0.127984 | − | 0.221674i | 0.794912 | − | 0.606725i | \(-0.207517\pi\) |
−0.922895 | + | 0.385051i | \(0.874184\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −768.312 | − | 1330.76i | −0.694164 | − | 1.20233i | −0.970462 | − | 0.241255i | \(-0.922441\pi\) |
0.276298 | − | 0.961072i | \(-0.410892\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −499.410 | + | 865.004i | −0.438852 | + | 0.760113i | −0.997601 | − | 0.0692232i | \(-0.977948\pi\) |
0.558750 | + | 0.829336i | \(0.311281\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −939.006 | −0.781719 | −0.390860 | − | 0.920450i | \(-0.627822\pi\) | ||||
−0.390860 | + | 0.920450i | \(0.627822\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −365.858 | + | 633.685i | −0.296665 | + | 0.513839i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 643.362 | + | 1114.34i | 0.483368 | + | 0.837217i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1454.09 | −1.04046 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1621.27 | −1.13279 | −0.566397 | − | 0.824133i | \(-0.691663\pi\) | ||||
−0.566397 | + | 0.824133i | \(0.691663\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 759.214 | + | 1315.00i | 0.506357 | + | 0.877037i | 0.999973 | + | 0.00735640i | \(0.00234164\pi\) |
−0.493616 | + | 0.869680i | \(0.664325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1242.50 | + | 2152.07i | −0.774844 | + | 1.34207i | 0.160038 | + | 0.987111i | \(0.448838\pi\) |
−0.934882 | + | 0.354958i | \(0.884495\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1655.36 | −1.01011 | −0.505057 | − | 0.863086i | \(-0.668529\pi\) | ||||
−0.505057 | + | 0.863086i | \(0.668529\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −252.630 | + | 437.568i | −0.147734 | + | 0.255883i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 467.673 | + | 810.033i | 0.267849 | + | 0.463928i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 175.095 | + | 303.274i | 0.0962709 | + | 0.166746i | 0.910138 | − | 0.414305i | \(-0.135975\pi\) |
−0.813867 | + | 0.581051i | \(0.802642\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1669.07 | + | 2890.91i | −0.899516 | + | 1.55801i | −0.0714022 | + | 0.997448i | \(0.522747\pi\) |
−0.828114 | + | 0.560560i | \(0.810586\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 668.799 | 0.346576 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 871.836 | − | 1510.06i | 0.443185 | − | 0.767620i | −0.554738 | − | 0.832025i | \(-0.687182\pi\) |
0.997924 | + | 0.0644052i | \(0.0205150\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1715.78 | − | 2971.82i | −0.824480 | − | 1.42804i | −0.902316 | − | 0.431076i | \(-0.858134\pi\) |
0.0778354 | − | 0.996966i | \(-0.475199\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3381.05 | −1.56667 | −0.783335 | − | 0.621600i | \(-0.786483\pi\) | ||||
−0.783335 | + | 0.621600i | \(0.786483\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3568.89 | 1.62444 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −670.501 | − | 1161.34i | −0.294666 | − | 0.510377i | 0.680241 | − | 0.732988i | \(-0.261875\pi\) |
−0.974907 | + | 0.222612i | \(0.928542\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 562.574 | − | 974.407i | 0.234909 | − | 0.406875i | −0.724337 | − | 0.689446i | \(-0.757854\pi\) |
0.959246 | + | 0.282571i | \(0.0911874\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3535.04 | −1.45170 | −0.725848 | − | 0.687855i | \(-0.758553\pi\) | ||||
−0.725848 | + | 0.687855i | \(0.758553\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −224.871 | + | 389.488i | −0.0893668 | + | 0.154788i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −346.962 | − | 600.956i | −0.135681 | − | 0.235007i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1319.95 | + | 2286.21i | 0.500041 | + | 0.866097i | 1.00000 | 4.78599e-5i | \(1.52343e-5\pi\) | |
−0.499959 | + | 0.866049i | \(0.666651\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −523.526 | + | 906.774i | −0.195255 | + | 0.338192i | −0.946984 | − | 0.321280i | \(-0.895887\pi\) |
0.751729 | + | 0.659472i | \(0.229220\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4585.45 | 1.65837 | 0.829187 | − | 0.558972i | \(-0.188804\pi\) | ||||
0.829187 | + | 0.558972i | \(0.188804\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −415.371 | + | 719.444i | −0.147964 | + | 0.256282i | −0.930475 | − | 0.366356i | \(-0.880605\pi\) |
0.782511 | + | 0.622637i | \(0.213939\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1672.33 | + | 2896.56i | 0.569759 | + | 0.986852i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 568.878 | 0.188278 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2630.08 | −0.858114 | −0.429057 | − | 0.903277i | \(-0.641154\pi\) | ||||
−0.429057 | + | 0.903277i | \(0.641154\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1633.37 | − | 2829.08i | −0.518116 | − | 0.897404i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3959.44 | + | 6857.94i | −1.20516 | + | 2.08740i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −863.988 | −0.259448 | −0.129724 | − | 0.991550i | \(-0.541409\pi\) | ||||
−0.129724 | + | 0.991550i | \(0.541409\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2080.18 | + | 3602.97i | −0.608221 | + | 1.05347i | 0.383312 | + | 0.923619i | \(0.374783\pi\) |
−0.991533 | + | 0.129851i | \(0.958550\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 90.6052 | + | 156.933i | 0.0261457 | + | 0.0452856i | 0.878802 | − | 0.477186i | \(-0.158343\pi\) |
−0.852657 | + | 0.522472i | \(0.825010\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1075.22 | + | 1862.34i | 0.302319 | + | 0.523631i | 0.976661 | − | 0.214788i | \(-0.0689060\pi\) |
−0.674342 | + | 0.738419i | \(0.735573\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1145.85 | − | 1984.67i | 0.318073 | − | 0.550918i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6939.47 | 1.87815 | 0.939073 | − | 0.343719i | \(-0.111687\pi\) | ||||
0.939073 | + | 0.343719i | \(0.111687\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 103.085 | − | 178.548i | 0.0275530 | − | 0.0477232i | −0.851920 | − | 0.523672i | \(-0.824562\pi\) |
0.879473 | + | 0.475949i | \(0.157895\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3245.94 | − | 5622.13i | −0.836171 | − | 1.44829i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5011.93 | −1.26036 | −0.630180 | − | 0.776449i | \(-0.717019\pi\) | ||||
−0.630180 | + | 0.776449i | \(0.717019\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 456.951 | 0.113551 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2931.54 | − | 5077.58i | −0.711535 | − | 1.23241i | −0.964281 | − | 0.264882i | \(-0.914667\pi\) |
0.252746 | − | 0.967533i | \(-0.418666\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2819.78 | + | 4884.00i | −0.661122 | + | 1.14510i | 0.319200 | + | 0.947688i | \(0.396586\pi\) |
−0.980321 | + | 0.197409i | \(0.936747\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5594.15 | −1.29678 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1488.32 | + | 2577.84i | −0.337339 | + | 0.584289i | −0.983931 | − | 0.178547i | \(-0.942860\pi\) |
0.646592 | + | 0.762836i | \(0.276194\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1403.67 | + | 2431.22i | 0.314637 | + | 0.544968i | 0.979360 | − | 0.202122i | \(-0.0647838\pi\) |
−0.664723 | + | 0.747090i | \(0.731450\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 38.1605 | + | 66.0959i | 0.00836787 | + | 0.0144936i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 959.194 | − | 1661.37i | 0.208059 | − | 0.360369i | −0.743044 | − | 0.669243i | \(-0.766619\pi\) |
0.951103 | + | 0.308874i | \(0.0999520\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5209.50 | −1.10595 | −0.552977 | − | 0.833197i | \(-0.686508\pi\) | ||||
−0.552977 | + | 0.833197i | \(0.686508\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3748.35 | + | 6492.33i | −0.787337 | + | 1.36371i | 0.140256 | + | 0.990115i | \(0.455207\pi\) |
−0.927593 | + | 0.373592i | \(0.878126\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2981.39 | − | 5163.92i | −0.606837 | − | 1.05107i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3358.94 | 0.669732 | 0.334866 | − | 0.942266i | \(-0.391309\pi\) | ||||
0.334866 | + | 0.942266i | \(0.391309\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3841.05 | −0.758084 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2607.30 | − | 4515.98i | −0.504294 | − | 0.873463i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4265.89 | + | 7388.73i | −0.800865 | + | 1.38714i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7330.92 | −1.36286 | −0.681429 | − | 0.731884i | \(-0.738641\pi\) | ||||
−0.681429 | + | 0.731884i | \(0.738641\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1019.27 | + | 1765.42i | −0.185843 | + | 0.321890i | −0.943860 | − | 0.330345i | \(-0.892835\pi\) |
0.758017 | + | 0.652235i | \(0.226168\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2069.44 | − | 3584.37i | −0.373711 | − | 0.647286i | 0.616423 | − | 0.787416i | \(-0.288581\pi\) |
−0.990133 | + | 0.140130i | \(0.955248\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3776.13 | − | 6540.44i | −0.669049 | − | 1.15883i | −0.978171 | − | 0.207804i | \(-0.933368\pi\) |
0.309122 | − | 0.951022i | \(-0.399965\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 292.058 | − | 505.859i | 0.0512605 | − | 0.0887858i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8915.94 | 1.53590 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 435.477 | − | 754.268i | 0.0743258 | − | 0.128736i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2788.85 | − | 4830.43i | −0.463109 | − | 0.802128i | 0.536005 | − | 0.844215i | \(-0.319933\pi\) |
−0.999114 | + | 0.0420865i | \(0.986599\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −428.637 | −0.0699073 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4467.16 | 0.722083 | 0.361041 | − | 0.932550i | \(-0.382421\pi\) | ||||
0.361041 | + | 0.932550i | \(0.382421\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −208.830 | − | 361.704i | −0.0331635 | − | 0.0574409i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4894.21 | − | 8477.01i | 0.757161 | − | 1.31144i | −0.187132 | − | 0.982335i | \(-0.559919\pi\) |
0.944293 | − | 0.329106i | \(-0.106747\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4746.95 | −0.728075 | −0.364038 | − | 0.931384i | \(-0.618602\pi\) | ||||
−0.364038 | + | 0.931384i | \(0.618602\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4717.33 | + | 8170.65i | −0.711269 | + | 1.23195i | 0.253112 | + | 0.967437i | \(0.418546\pi\) |
−0.964381 | + | 0.264517i | \(0.914787\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1591.76 | − | 2757.01i | −0.237977 | − | 0.412189i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5653.77 | + | 9792.62i | 0.831183 | + | 1.43965i | 0.897101 | + | 0.441826i | \(0.145669\pi\) |
−0.0659178 | + | 0.997825i | \(0.520998\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −225.138 | + | 389.950i | −0.0328237 | + | 0.0568523i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5510.00 | 0.790155 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3044.80 | + | 5273.76i | −0.433072 | + | 0.750103i | −0.997136 | − | 0.0756282i | \(-0.975904\pi\) |
0.564064 | + | 0.825731i | \(0.309237\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1300.92 | + | 2253.26i | 0.180588 | + | 0.312787i | 0.942081 | − | 0.335386i | \(-0.108867\pi\) |
−0.761493 | + | 0.648173i | \(0.775533\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6665.77 | −0.910622 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10416.2 | 1.41173 | 0.705865 | − | 0.708347i | \(-0.250559\pi\) | ||||
0.705865 | + | 0.708347i | \(0.250559\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −832.230 | − | 1441.47i | −0.111031 | − | 0.192312i | 0.805155 | − | 0.593064i | \(-0.202082\pi\) |
−0.916186 | + | 0.400753i | \(0.868749\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −667.078 | + | 1155.41i | −0.0869465 | + | 0.150596i | −0.906219 | − | 0.422809i | \(-0.861044\pi\) |
0.819272 | + | 0.573404i | \(0.194378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7161.73 | 0.926302 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6512.71 | − | 11280.4i | 0.829596 | − | 1.43690i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2222.44 | − | 3849.38i | −0.280960 | − | 0.486637i | 0.690662 | − | 0.723178i | \(-0.257319\pi\) |
−0.971621 | + | 0.236541i | \(0.923986\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1324.91 | − | 2294.81i | −0.164995 | − | 0.285779i | 0.771659 | − | 0.636037i | \(-0.219427\pi\) |
−0.936653 | + | 0.350258i | \(0.886094\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2383.11 | + | 4127.66i | −0.294568 | + | 0.510207i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 280.860 | 0.0342057 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4796.33 | − | 8307.49i | 0.579862 | − | 1.00435i | −0.415633 | − | 0.909532i | \(-0.636440\pi\) |
0.995495 | − | 0.0948173i | \(-0.0302267\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7077.89 | + | 12259.3i | 0.837205 | + | 1.45008i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16850.1 | −1.96463 | −0.982317 | − | 0.187224i | \(-0.940051\pi\) | ||||
−0.982317 | + | 0.187224i | \(0.940051\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1691.10 | 0.195770 | 0.0978849 | − | 0.995198i | \(-0.468792\pi\) | ||||
0.0978849 | + | 0.995198i | \(0.468792\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 598.084 | + | 1035.91i | 0.0682619 | + | 0.118233i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3394.67 | + | 5879.74i | −0.379386 | + | 0.657117i | −0.990973 | − | 0.134061i | \(-0.957198\pi\) |
0.611587 | + | 0.791177i | \(0.290532\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10386.6 | 1.15276 | 0.576382 | − | 0.817180i | \(-0.304464\pi\) | ||||
0.576382 | + | 0.817180i | \(0.304464\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2935.59 | + | 5084.58i | −0.321346 | + | 0.556587i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2106.13 | + | 3647.92i | 0.228975 | + | 0.396596i | 0.957505 | − | 0.288418i | \(-0.0931292\pi\) |
−0.728530 | + | 0.685014i | \(0.759796\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −904.980 | − | 1567.47i | −0.0970585 | − | 0.168110i | 0.813407 | − | 0.581694i | \(-0.197610\pi\) |
−0.910466 | + | 0.413584i | \(0.864277\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3409.28 | + | 5905.05i | −0.363181 | + | 0.629048i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1768.29 | −0.185859 | −0.0929297 | − | 0.995673i | \(-0.529623\pi\) | ||||
−0.0929297 | + | 0.995673i | \(0.529623\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1044.36 | − | 1808.88i | 0.109040 | − | 0.188862i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2186.30 | − | 3786.79i | −0.223788 | − | 0.387611i | 0.732167 | − | 0.681125i | \(-0.238509\pi\) |
−0.955955 | + | 0.293513i | \(0.905176\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1164.34 | 0.117633 | 0.0588165 | − | 0.998269i | \(-0.481267\pi\) | ||||
0.0588165 | + | 0.998269i | \(0.481267\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14893.9 | −1.49498 | −0.747491 | − | 0.664272i | \(-0.768742\pi\) | ||||
−0.747491 | + | 0.664272i | \(0.768742\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9580.14 | + | 16593.3i | 0.949285 | + | 1.64421i | 0.746936 | + | 0.664896i | \(0.231524\pi\) |
0.202349 | + | 0.979314i | \(0.435143\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1020.03 | + | 1766.74i | −0.0991562 | + | 0.171744i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −980.616 | −0.0947237 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4703.14 | + | 8146.08i | −0.448626 | + | 0.777043i | −0.998297 | − | 0.0583380i | \(-0.981420\pi\) |
0.549671 | + | 0.835381i | \(0.314753\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1602.55 | − | 2775.70i | −0.151913 | − | 0.263121i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7595.19 | − | 13155.3i | −0.711092 | − | 1.23165i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6230.39 | + | 10791.4i | −0.579725 | + | 1.00411i | 0.415786 | + | 0.909463i | \(0.363507\pi\) |
−0.995511 | + | 0.0946505i | \(0.969827\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12868.0 | −1.18274 | −0.591369 | − | 0.806401i | \(-0.701412\pi\) | ||||
−0.591369 | + | 0.806401i | \(0.701412\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4577.38 | − | 7928.26i | 0.418164 | − | 0.724281i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6852.50 | + | 11868.9i | 0.614750 | + | 1.06478i | 0.990428 | + | 0.138028i | \(0.0440763\pi\) |
−0.375679 | + | 0.926750i | \(0.622590\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10126.1 | −0.897616 | −0.448808 | − | 0.893628i | \(-0.648151\pi\) | ||||
−0.448808 | + | 0.893628i | \(0.648151\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10571.6 | 0.931546 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3118.03 | − | 5400.59i | −0.271521 | − | 0.470288i | 0.697730 | − | 0.716360i | \(-0.254193\pi\) |
−0.969252 | + | 0.246072i | \(0.920860\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1425.50 | + | 2469.03i | −0.121971 | + | 0.211259i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1431.15 | −0.121744 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8508.38 | − | 14737.0i | 0.715468 | − | 1.23923i | −0.247310 | − | 0.968936i | \(-0.579547\pi\) |
0.962779 | − | 0.270291i | \(-0.0871200\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2907.31 | + | 5035.61i | 0.243074 | + | 0.421017i | 0.961588 | − | 0.274496i | \(-0.0885109\pi\) |
−0.718514 | + | 0.695512i | \(0.755178\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3272.96 | − | 5668.93i | −0.270536 | − | 0.468582i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3725.49 | − | 6452.74i | 0.306196 | − | 0.530348i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23835.8 | −1.93704 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8186.41 | + | 14179.3i | −0.661550 | + | 1.14584i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5034.59 | + | 8720.17i | 0.400100 | + | 0.692993i | 0.993738 | − | 0.111739i | \(-0.0356421\pi\) |
−0.593638 | + | 0.804732i | \(0.702309\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10642.5 | 0.836466 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7437.51 | −0.581362 | −0.290681 | − | 0.956820i | \(-0.593882\pi\) | ||||
−0.290681 | + | 0.956820i | \(0.593882\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3752.53 | + | 6499.57i | 0.290133 | + | 0.502525i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10893.6 | − | 18868.2i | 0.828680 | − | 1.43532i | −0.0703944 | − | 0.997519i | \(-0.522426\pi\) |
0.899074 | − | 0.437796i | \(-0.144241\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23280.5 | 1.76147 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1286.24 | − | 2227.83i | 0.0962851 | − | 0.166771i | −0.813859 | − | 0.581062i | \(-0.802637\pi\) |
0.910144 | + | 0.414292i | \(0.135971\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5002.58 | + | 8664.72i | 0.372496 | + | 0.645181i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8790.29 | − | 15225.2i | −0.647642 | − | 1.12175i | −0.983685 | − | 0.179902i | \(-0.942422\pi\) |
0.336043 | − | 0.941847i | \(-0.390911\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3610.37 | + | 6253.35i | −0.264605 | + | 0.458309i | −0.967460 | − | 0.253024i | \(-0.918575\pi\) |
0.702855 | + | 0.711333i | \(0.251908\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −787.679 | −0.0571278 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5577.54 | + | 9660.58i | −0.402419 | + | 0.697011i | −0.994017 | − | 0.109222i | \(-0.965164\pi\) |
0.591598 | + | 0.806233i | \(0.298497\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1746.75 | + | 3025.46i | 0.124088 | + | 0.214926i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15216.2 | 1.06992 | 0.534958 | − | 0.844879i | \(-0.320327\pi\) | ||||
0.534958 | + | 0.844879i | \(0.320327\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5366.33 | 0.375409 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1921.95 | + | 3328.91i | 0.133094 | + | 0.230526i | 0.924868 | − | 0.380289i | \(-0.124175\pi\) |
−0.791774 | + | 0.610815i | \(0.790842\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9373.48 | − | 16235.3i | 0.639382 | − | 1.10744i | −0.346186 | − | 0.938166i | \(-0.612524\pi\) |
0.985569 | − | 0.169277i | \(-0.0541431\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9864.63 | −0.669529 | −0.334764 | − | 0.942302i | \(-0.608657\pi\) | ||||
−0.334764 | + | 0.942302i | \(0.608657\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6855.06 | − | 11873.3i | 0.460657 | − | 0.797882i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11146.4 | − | 19306.2i | −0.745336 | − | 1.29096i | −0.950038 | − | 0.312136i | \(-0.898956\pi\) |
0.204701 | − | 0.978824i | \(-0.434378\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8165.94 | + | 14143.8i | 0.540685 | + | 0.936494i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3023.39 | + | 5236.67i | −0.199206 | + | 0.345036i | −0.948271 | − | 0.317461i | \(-0.897170\pi\) |
0.749065 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9383.68 | 0.612273 | 0.306137 | − | 0.951988i | \(-0.400964\pi\) | ||||
0.306137 | + | 0.951988i | \(0.400964\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1994.75 | − | 3455.00i | 0.129525 | − | 0.224343i | −0.793968 | − | 0.607960i | \(-0.791988\pi\) |
0.923492 | + | 0.383617i | \(0.125322\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7029.85 | + | 12176.1i | 0.449910 | + | 0.779267i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4401.88 | 0.279038 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11434.0 | 0.721363 | 0.360681 | − | 0.932689i | \(-0.382544\pi\) | ||||
0.360681 | + | 0.932689i | \(0.382544\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8637.37 | + | 14960.4i | 0.539785 | + | 0.934935i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7548.63 | + | 13074.6i | −0.465137 | + | 0.805641i | −0.999208 | − | 0.0397989i | \(-0.987328\pi\) |
0.534071 | + | 0.845440i | \(0.320662\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4170.19 | 0.255764 | 0.127882 | − | 0.991789i | \(-0.459182\pi\) | ||||
0.127882 | + | 0.991789i | \(0.459182\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2281.94 | + | 3952.44i | −0.138659 | + | 0.240164i | −0.926989 | − | 0.375088i | \(-0.877613\pi\) |
0.788330 | + | 0.615252i | \(0.210946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1199.35 | + | 2077.34i | 0.0725404 | + | 0.125644i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1909.52 | + | 3307.39i | 0.114434 | + | 0.198205i | 0.917553 | − | 0.397613i | \(-0.130161\pi\) |
−0.803119 | + | 0.595818i | \(0.796828\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8089.46 | − | 14011.4i | 0.482567 | − | 0.835830i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4326.02 | 0.255717 | 0.127859 | − | 0.991792i | \(-0.459190\pi\) | ||||
0.127859 | + | 0.991792i | \(0.459190\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14658.9 | − | 25389.9i | 0.862579 | − | 1.49403i | −0.00685243 | − | 0.999977i | \(-0.502181\pi\) |
0.869431 | − | 0.494054i | \(-0.164485\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3014.22 | + | 5220.78i | 0.174979 | + | 0.303072i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5328.02 | 0.306536 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5483.56 | −0.314080 | −0.157040 | − | 0.987592i | \(-0.550195\pi\) | ||||
−0.157040 | + | 0.987592i | \(0.550195\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6034.67 | − | 10452.4i | −0.342587 | − | 0.593378i | 0.642325 | − | 0.766432i | \(-0.277970\pi\) |
−0.984912 | + | 0.173054i | \(0.944636\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15398.4 | − | 26670.7i | 0.862667 | − | 1.49418i | −0.00667825 | − | 0.999978i | \(-0.502126\pi\) |
0.869345 | − | 0.494205i | \(-0.164541\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26477.7 | 1.47688 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19933.4 | − | 34525.7i | 1.10218 | − | 1.90903i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3250.98 | + | 5630.87i | 0.178977 | + | 0.309997i | 0.941530 | − | 0.336928i | \(-0.109388\pi\) |
−0.762553 | + | 0.646925i | \(0.776055\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8818.98 | + | 15274.9i | 0.481328 | + | 0.833685i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16368.0 | − | 28350.3i | 0.889504 | − | 1.54067i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2235.98 | 0.120473 | 0.0602367 | − | 0.998184i | \(-0.480814\pi\) | ||||
0.0602367 | + | 0.998184i | \(0.480814\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1804.33 | + | 3125.19i | −0.0968016 | + | 0.167665i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17782.2 | − | 30799.7i | −0.941926 | − | 1.63146i | −0.761792 | − | 0.647822i | \(-0.775680\pi\) |
−0.180134 | − | 0.983642i | \(-0.557653\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4310.50 | 0.226409 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5383.57 | 0.281586 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4962.07 | − | 8594.56i | −0.257377 | − | 0.445790i | 0.708161 | − | 0.706051i | \(-0.249525\pi\) |
−0.965538 | + | 0.260260i | \(0.916192\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −503.441 | + | 871.985i | −0.0257894 | + | 0.0446686i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 880.081 | 0.0448974 | 0.0224487 | − | 0.999748i | \(-0.492854\pi\) | ||||
0.0224487 | + | 0.999748i | \(0.492854\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15986.7 | + | 27689.8i | −0.808879 | + | 1.40102i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8668.08 | + | 15013.5i | 0.436784 | + | 0.756532i | 0.997439 | − | 0.0715172i | \(-0.0227841\pi\) |
−0.560655 | + | 0.828049i | \(0.689451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 133.840 | + | 231.818i | 0.00668937 | + | 0.0115863i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12293.2 | − | 21292.4i | 0.611924 | − | 1.05988i | −0.378992 | − | 0.925400i | \(-0.623729\pi\) |
0.990916 | − | 0.134483i | \(-0.0429375\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14579.3 | −0.719870 | −0.359935 | − | 0.932977i | \(-0.617201\pi\) | ||||
−0.359935 | + | 0.932977i | \(0.617201\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1865.65 | − | 3231.40i | 0.0917478 | − | 0.158912i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8042.98 | − | 13930.8i | −0.390802 | − | 0.676889i | 0.601753 | − | 0.798682i | \(-0.294469\pi\) |
−0.992556 | + | 0.121793i | \(0.961136\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 35568.0 | 1.71451 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37017.3 | −1.77730 | −0.888651 | − | 0.458584i | \(-0.848357\pi\) | ||||
−0.888651 | + | 0.458584i | \(0.848357\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12303.2 | + | 21309.8i | 0.586060 | + | 1.01509i | 0.994742 | + | 0.102410i | \(0.0326552\pi\) |
−0.408682 | + | 0.912677i | \(0.634011\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13686.7 | − | 23706.0i | 0.644325 | − | 1.11600i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12715.6 | −0.596275 | −0.298137 | − | 0.954523i | \(-0.596365\pi\) | ||||
−0.298137 | + | 0.954523i | \(0.596365\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1587.11 | − | 2748.96i | 0.0738480 | − | 0.127908i | −0.826737 | − | 0.562589i | \(-0.809805\pi\) |
0.900585 | + | 0.434681i | \(0.143139\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 359.975 | + | 623.495i | 0.0166847 | + | 0.0288988i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13418.5 | + | 23241.5i | 0.617160 | + | 1.06895i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −994.042 | + | 1721.73i | −0.0455437 | + | 0.0788840i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18578.9 | −0.844726 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7784.94 | − | 13483.9i | 0.352609 | − | 0.610736i | −0.634097 | − | 0.773254i | \(-0.718628\pi\) |
0.986706 | + | 0.162517i | \(0.0519613\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30400.9 | − | 52656.0i | −1.36137 | − | 2.35797i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31514.5 | 1.40063 | 0.700314 | − | 0.713835i | \(-0.253043\pi\) | ||||
0.700314 | + | 0.713835i | \(0.253043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22430.2 | −0.993146 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1720.48 | − | 2979.95i | −0.0756093 | − | 0.130959i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5514.54 | − | 9551.47i | 0.239655 | − | 0.415095i | −0.720960 | − | 0.692976i | \(-0.756299\pi\) |
0.960615 | + | 0.277882i | \(0.0896323\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20830.5 | −0.901920 | −0.450960 | − | 0.892544i | \(-0.648918\pi\) | ||||
−0.450960 | + | 0.892544i | \(0.648918\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18281.7 | + | 31664.9i | −0.785743 | + | 1.36095i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13105.9 | − | 22700.1i | −0.561221 | − | 0.972063i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4674.53 | − | 8096.53i | −0.198712 | − | 0.344179i | 0.749399 | − | 0.662118i | \(-0.230342\pi\) |
−0.948111 | + | 0.317940i | \(0.897009\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16445.3 | − | 28484.1i | 0.696533 | − | 1.20643i | −0.273129 | − | 0.961978i | \(-0.588058\pi\) |
0.969661 | − | 0.244452i | \(-0.0786082\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13081.2 | 0.550033 | 0.275016 | − | 0.961440i | \(-0.411317\pi\) | ||||
0.275016 | + | 0.961440i | \(0.411317\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14395.6 | + | 24933.9i | −0.603112 | + | 1.04462i | 0.389235 | + | 0.921138i | \(0.372739\pi\) |
−0.992347 | + | 0.123482i | \(0.960594\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18012.6 | + | 31198.8i | 0.746531 | + | 1.29303i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36766.8 | 1.51291 | 0.756455 | − | 0.654046i | \(-0.226930\pi\) | ||||
0.756455 | + | 0.654046i | \(0.226930\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16682.9 | −0.684034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19013.4 | − | 32932.1i | −0.774058 | − | 1.34071i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1449.33 | + | 2510.31i | −0.0583810 | + | 0.101119i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5899.55 | 0.236808 | 0.118404 | − | 0.992966i | \(-0.462222\pi\) | ||||
0.118404 | + | 0.992966i | \(0.462222\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21138.5 | − | 36613.0i | 0.842564 | − | 1.45936i | −0.0451553 | − | 0.998980i | \(-0.514378\pi\) |
0.887720 | − | 0.460384i | \(-0.152288\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3171.73 | + | 5493.59i | 0.125981 | + | 0.218206i | 0.922116 | − | 0.386913i | \(-0.126459\pi\) |
−0.796135 | + | 0.605119i | \(0.793125\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3464.89 | + | 6001.36i | 0.136670 | + | 0.236719i | 0.926234 | − | 0.376949i | \(-0.123027\pi\) |
−0.789564 | + | 0.613668i | \(0.789693\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7144.22 | + | 12374.1i | −0.280822 | + | 0.486397i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8134.27 | −0.317533 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1527.35 | − | 2645.44i | 0.0594170 | − | 0.102913i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1643.94 | − | 2847.39i | −0.0632976 | − | 0.109635i | 0.832640 | − | 0.553815i | \(-0.186828\pi\) |
−0.895938 | + | 0.444180i | \(0.853495\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46875.9 | 1.79261 | 0.896304 | − | 0.443439i | \(-0.146242\pi\) | ||||
0.896304 | + | 0.443439i | \(0.146242\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42479.4 | 1.61897 | 0.809483 | − | 0.587144i | \(-0.199748\pi\) | ||||
0.809483 | + | 0.587144i | \(0.199748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1840.08 | + | 3187.11i | 0.0696547 | + | 0.120645i | 0.898749 | − | 0.438463i | \(-0.144477\pi\) |
−0.829095 | + | 0.559108i | \(0.811144\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9194.12 | − | 15924.7i | 0.344535 | − | 0.596752i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11988.5 | −0.447745 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2755.04 | − | 4771.86i | 0.102209 | − | 0.177031i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27376.6 | + | 47417.6i | 1.01226 | + | 1.75328i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18833.0 | + | 32619.7i | 0.691745 | + | 1.19814i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3551.09 | − | 6150.67i | 0.130002 | − | 0.225171i | −0.793675 | − | 0.608342i | \(-0.791835\pi\) |
0.923677 | + | 0.383172i | \(0.125168\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38119.0 | −1.38632 | −0.693161 | − | 0.720783i | \(-0.743782\pi\) | ||||
−0.693161 | + | 0.720783i | \(0.743782\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4420.08 | − | 7655.81i | 0.160223 | − | 0.277514i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8595.28 | − | 14887.5i | −0.308522 | − | 0.534377i | 0.669517 | − | 0.742797i | \(-0.266501\pi\) |
−0.978039 | + | 0.208420i | \(0.933168\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22687.5 | 0.809065 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −484.139 | −0.0172091 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16128.2 | + | 27934.9i | 0.569591 | + | 0.986561i | 0.996606 | + | 0.0823167i | \(0.0262319\pi\) |
−0.427015 | + | 0.904245i | \(0.640435\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3696.90 | + | 6403.22i | −0.129306 | + | 0.223965i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26213.6 | 0.913940 | 0.456970 | − | 0.889482i | \(-0.348935\pi\) | ||||
0.456970 | + | 0.889482i | \(0.348935\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17120.0 | − | 29652.8i | 0.593089 | − | 1.02726i | −0.400724 | − | 0.916199i | \(-0.631241\pi\) |
0.993813 | − | 0.111062i | \(-0.0354252\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10778.4 | + | 18668.7i | 0.372209 | + | 0.644685i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18002.3 | + | 31180.8i | 0.617735 | + | 1.06995i | 0.989898 | + | 0.141781i | \(0.0452828\pi\) |
−0.372163 | + | 0.928167i | \(0.621384\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19633.6 | + | 34006.4i | −0.671584 | + | 1.16322i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29488.1 | 1.00232 | 0.501161 | − | 0.865354i | \(-0.332907\pi\) | ||||
0.501161 | + | 0.865354i | \(0.332907\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14064.1 | − | 24359.7i | 0.476548 | − | 0.825405i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12925.6 | + | 22387.7i | 0.433875 | + | 0.751494i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11156.4 | 0.372163 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56009.0 | −1.86260 | −0.931298 | − | 0.364259i | \(-0.881322\pi\) | ||||
−0.931298 | + | 0.364259i | \(0.881322\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6788.44 | + | 11757.9i | 0.224358 | + | 0.388599i | 0.956127 | − | 0.292954i | \(-0.0946383\pi\) |
−0.731769 | + | 0.681553i | \(0.761305\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15887.6 | + | 27518.1i | −0.520254 | + | 0.901107i | 0.479468 | + | 0.877559i | \(0.340829\pi\) |
−0.999723 | + | 0.0235477i | \(0.992504\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4258.14 | 0.139010 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16377.7 | − | 28367.0i | 0.531401 | − | 0.920414i | −0.467927 | − | 0.883767i | \(-0.654999\pi\) |
0.999328 | − | 0.0366471i | \(-0.0116677\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24429.1 | − | 42312.4i | −0.790228 | − | 1.36872i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10527.3 | − | 18233.8i | −0.338472 | − | 0.586251i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20398.5 | − | 35331.3i | 0.653865 | − | 1.13253i | −0.328312 | − | 0.944569i | \(-0.606480\pi\) |
0.982177 | − | 0.187958i | \(-0.0601869\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8851.60 | 0.282025 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8685.25 | − | 15043.3i | 0.275892 | − | 0.477859i | −0.694468 | − | 0.719524i | \(-0.744360\pi\) |
0.970360 | + | 0.241665i | \(0.0776934\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1764.4.k.bd.361.2 | 8 | ||
3.2 | odd | 2 | 588.4.i.k.361.3 | 8 | |||
7.2 | even | 3 | inner | 1764.4.k.bd.1549.2 | 8 | ||
7.3 | odd | 6 | 1764.4.a.bc.1.2 | 4 | |||
7.4 | even | 3 | 1764.4.a.ba.1.3 | 4 | |||
7.5 | odd | 6 | 1764.4.k.bb.1549.3 | 8 | |||
7.6 | odd | 2 | 1764.4.k.bb.361.3 | 8 | |||
21.2 | odd | 6 | 588.4.i.k.373.3 | 8 | |||
21.5 | even | 6 | 588.4.i.l.373.2 | 8 | |||
21.11 | odd | 6 | 588.4.a.k.1.2 | yes | 4 | ||
21.17 | even | 6 | 588.4.a.j.1.3 | ✓ | 4 | ||
21.20 | even | 2 | 588.4.i.l.361.2 | 8 | |||
84.11 | even | 6 | 2352.4.a.cl.1.2 | 4 | |||
84.59 | odd | 6 | 2352.4.a.cq.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.a.j.1.3 | ✓ | 4 | 21.17 | even | 6 | ||
588.4.a.k.1.2 | yes | 4 | 21.11 | odd | 6 | ||
588.4.i.k.361.3 | 8 | 3.2 | odd | 2 | |||
588.4.i.k.373.3 | 8 | 21.2 | odd | 6 | |||
588.4.i.l.361.2 | 8 | 21.20 | even | 2 | |||
588.4.i.l.373.2 | 8 | 21.5 | even | 6 | |||
1764.4.a.ba.1.3 | 4 | 7.4 | even | 3 | |||
1764.4.a.bc.1.2 | 4 | 7.3 | odd | 6 | |||
1764.4.k.bb.361.3 | 8 | 7.6 | odd | 2 | |||
1764.4.k.bb.1549.3 | 8 | 7.5 | odd | 6 | |||
1764.4.k.bd.361.2 | 8 | 1.1 | even | 1 | trivial | ||
1764.4.k.bd.1549.2 | 8 | 7.2 | even | 3 | inner | ||
2352.4.a.cl.1.2 | 4 | 84.11 | even | 6 | |||
2352.4.a.cq.1.3 | 4 | 84.59 | odd | 6 |